基于扩展阻抗模态分析的逆变器频率支撑强度量化评估

doi:10.19595/j.cnki.1000-6753.tces.250740

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Abstract With the large-scale integration of high-proportion inverter-based resources (IBRs), the synchronous dynamic (SD) characteristics of modern power systems have undergone significant changes. The reduction in system equivalent inertia results in more severe frequency fluctuations, posing new challenges to frequency security and stability. Based on flexible control algorithms, these IBRs are mainly categorized into grid-forming inverters (GFMs) and grid-following inverters (GFLs). The distinct external characteristics of GFMs and GFLs further complicate the analysis of frequency stability in power systems.
To quantitatively analyze the frequency support strength of IBRs, it is essential to consider the impact of various influencing factors on system stability. Modal Analysis based on the state-space model (MASS) quantifies the contribution of each state variable to a specific mode using the participation factor (PF). However, issues such as the black-box nature of the model and the curse of dimensionality limit its applicability in large-scale systems. Currently, impedance-based analysis methods have been widely discussed. Based on the whole-system dynamic admittance matrix and dynamic impedance matrix, the modal analysis based on impedance model (MAI) method introduces the impedance participation factor (IPF) and the admittance participation factor (APF). IPF and APF treat IBRs as a whole, considering their overall dynamic impact on system stability. As a result, MAI cannot provide detailed insights into the internal dynamics of IBRs.
To address the control characteristics of GFMs, the impedance-based extended modal analysis (EMAI) method classifies the GFM dynamics into SD, dominated by the power frequency synchronization loop (PFL), and electromagnetic dynamics (ED), governed by the voltage control loop (VCL). For GFLs, the admittance- based EMAI method categorizes their dynamics into SD, dominated by the phase-locked loop (PLL), and ED, governed by the current control loop (CCL). However, the relationship between the impedance-based EMAI and the admittance-based EMAI remains unclear. Moreover, in large-scale systems, multiple oscillatory modes with weak damping may exist, and the SD of different IBRs may contribute to these modes. As a result, EMAI alone may not be sufficient for directly and equitably assessing the frequency support capability of different IBRs.
This paper proposes an accurate evaluation method for IBR frequency support strength based on EMAI. First, the unification of the IPF and APF is demonstrated, thereby extending the applicability of the EMAI method to analyze the internal ED and SD of IBRs in hybrid power systems that contain GFMs and GFLs. Subsequently, based on EMAI, the maximum perturbation level of the dominant SD mode in IBRs is calculated to define the frequency support margin (FSM), which determines the frequency support strength of IBRs. Then, FSM is used to analyze the impact of different improvement measures on the frequency support strength of IBRs. Finally, simulations of a single GFM/GFL infinite system and a modified IEEE 14-bus system are conducted. Depending on data availability, the proposed method can adopt either a data-driven or model-driven approach, making it highly applicable in engineering practice.
The unified EMAI enables the analysis of internal SD in different types of IBRs, without being restricted to specific frequency response ports, allowing for direct extraction from widely used impedance/admittance models. For GFMs, lower grid impedance, reduced proportional and integral gains of the VCL (narrower VCL bandwidth), and higher PFL droop gains lead to a decrease in frequency support strength. For GFLs, higher grid impedance, reduced proportional and integral gains of the CCL (resulting in a narrower CCL bandwidth), and increased proportional and integral gains of the PFL (resulting in a wider CCL bandwidth) contribute to a reduction in frequency support strength.

Key words： Frequency support strength synchronous dynamic participation factor anti-disturbance capa- bility impedance model

Received: 30 April 2025

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TM614

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	Zheng Jiajie
	Zheng Le
	Lin Jiajian
	Xu Hui
	Liu Chongru

Cite this article:

Zheng Jiajie,Zheng Le,Lin Jiajian等. Quantitative Evaluation of Inverter Frequency Support Strength Based on Extended Impedance Modal Analysis[J]. Transactions of China Electrotechnical Society, 2026, 41(8): 2788-2804.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.250740 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I8/2788

[1] Hong Qiteng, Khan M A U, Henderson C, et al. Addressing frequency control challenges in future low-inertia power systems: a great Britain perspe-ctive[J]. Engineering, 2021, 7(8): 1057-1063.
[2] Sun Shitao, Lei Yu, Hao Guowen, et al.Transient damping of virtual synchronous generator for enhancing synchronization stability during voltage dips[J]. CES Transactions on Electrical Machines and Systems, 2024, 8(2): 143-151.
[3] Pang Bo, Si Qi, Jiang Pan, et al.Review of the analysis and suppression for high-frequency oscillations of the grid-connected wind power generation system[J]. CES Transactions on Electrical Machines and Systems, 2024, 8(2): 127-142.
[4] 黄萌, 舒思睿, 李锡林, 等. 面向同步稳定性的电力电子并网变流器分析与控制研究综述[J]. 电工技术学报, 2024, 39(19): 5978-5994.
Huang Meng, Shu Sirui, Li Xilin, et al.A review of synchronization-stability-oriented analysis and control of power electronic grid-connected converters[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 5978-5994.
[5] Hatziargyriou N, Milanovic J, Rahmann C, et al.Definition and classification of power system stability-revisited & extended[J]. IEEE Transactions on Power Systems, 2021, 36(4): 3271-3281.
[6] Gu Yunjie, Green T C.Power system stability with a high penetration of inverter-based resources[J]. Pro-ceedings of the IEEE, 2023, 111(7): 832-853.
[7] 闵勇, 陈磊, 刘瑞阔, 等. 电力系统频率动态中惯量与惯量响应特性辨析[J]. 中国电机工程学报, 2023, 43(3): 855-868.
Min Yong, Chen Lei, Liu Ruikuo, et al.Analysis on characteristics of inertia and inertial response in power system frequency dynamics[J]. Proceedings of the CSEE, 2023, 43(3): 855-868.
[8] 胡光, 庄可好, 高晖胜, 等. 低惯量交流系统并网变流器次/超同步振荡分析[J]. 电工技术学报, 2024, 39(8): 2250-2264.
Hu Guang, Zhuang Kehao, Gao Huisheng, et al.Sub/super synchronous oscillation analysis of grid connected converter in low inertia AC system[J]. Transactions of China Electrotechnical Society, 2024, 39(8): 2250-2264.
[9] 张怡静, 李智, 时艳强, 等. 基于储能惯量支撑的受端电网频率优化控制方法[J]. 电工技术学报, 2024, 39(11): 3556-3568.
Zhang Yijing, Li Zhi, Shi Yanqiang, et al.Optimal frequency control method of receiving power grid based on energy storage inertia support[J]. Transa-ctions of China Electrotechnical Society, 2024, 39(11): 3556-3568.
[10] Li Yitong, Gu Yunjie, Green T C.Revisiting grid-forming and grid-following inverters: a duality theory[J]. IEEE Transactions on Power Systems, 2022, 37(6): 4541-4554.
[11] Hu Pengfei, Li Yujing, Yu Yanxue, et al.Inertia estimation of renewable-energy-dominated power system[J]. Renewable and Sustainable Energy Reviews, 2023, 183: 113481.
[12] 孙华东, 赵兵, 徐式蕴, 等. 高比例电力电子电力系统强度的定义、分类及分析方法[J]. 中国电机工程学报, 2024, 44(18): 7039-7049.
Sun Huadong, Zhao Bing, Xu Shiyun, et al.Definition, classification, and analysis method of the strength of power system integrated with high penetration of power electronics[J]. Proceedings of the CSEE, 2024, 44(18): 7039-7049.
[13] 丁磊, 郭一忱, 鲍威宇, 等. 能量视角下的电力系统惯量[J]. 电力系统自动化, 2024, 48(8): 3-13.
Ding Lei, Guo Yichen, Bao Weiyu, et al.Inertia of power systems from energy perspective[J]. Auto-mation of Electric Power Systems, 2024, 48(8): 3-13.
[14] 颜湘武, 贾焦心, 王德胜, 等. 基于P/ω“导纳”的并联虚拟同步机功频响应建模与分析[J]. 电工技术学报, 2020, 35(15): 3191-3202.
Yan Xiangwu, Jia Jiaoxin, Wang Desheng, et al.Modeling and analysis of active power-frequency response of parallel VSGs using a P/ω “admittance”[J]. Transactions of China Electrotechnical Society, 2020, 35(15): 3191-3202.
[15] 胡光, 高晖胜, 辛焕海, 等. 考虑惯量模态特征的电力系统频率性能量化方法[J]. 中国电机工程学报, 2023, 43(22): 8559-8569.
Hu Guang, Gao Huisheng, Xin Huanhai, et al.A Quantification method for frequency performance of power system considering modal feature of inertia[J]. Proceedings of the CSEE, 2023, 43(22): 8559-8569.
[16] 马宁嘉, 谢小荣, 李浩志, 等. 计及频率动态分布性的新能源机组惯量需求分析[J]. 中国电机工程学报, 2024, 44(9): 3500-3508.
Ma Ningjia, Xie Xiaorong, Li Haozhi, et al.Inertial requirements for renewable energy units considering the space-time distribution characteristics of frequ-ency[J]. Proceedings of the CSEE, 2024, 44(9): 3500-3508.
[17] Yang Deyou, Wang Bo, Cai Guowei, et al.Data-driven estimation of inertia for multiarea inter-connected power systems using dynamic mode decomposition[J]. IEEE Transactions on Industrial Informatics, 2021, 17(4): 2686-2695.
[18] Linaro D, Bizzarri F, del Giudice D, et al. Continuous stimation of power system inertia using convolutional neural networks[J]. Nature Communications, 2023, 14: 4440.
[19] 刘其泳, 于之虹, 张璐路, 等. 基于惯量比的电网频率支撑能力在线评估方法[J]. 电网技术, 2023, 47(2): 493-502.
Liu Qiyong, Yu Zhihong, Zhang Lulu, et al.Online frequency support capacity assessment of power grid based on inertia ratio[J]. Power System Technology, 2023, 47(2): 493-502.
[20] Abouyehia M, Egea-Àlvarez A, Aphale S S, et al. Novel frequency-domain inertia mapping and esti-mation in power systems using wavelet analysis[J]. IEEE Transactions on Power Systems, 2025, 40(3): 2557-2567.
[21] 马燕峰, 李金媛, 王子建, 等. 基于量测数据的新能源电力系统区域等效惯量评估方法[J]. 电工技术学报, 2024, 39(17): 5406-5421.
Ma Yanfeng, Li Jinyuan, Wang Zijian, et al.Assessment method of regional equivalent inertia of new energy power system based on measured data[J]. Transactions of China Electrotechnical Society, 2024, 39(17): 5406-5421.
[22] 胡光, 高晖胜, 辛焕海, 等. 考虑电压动态的电力系统频率强度量化方法[J]. 电力系统自动化, 2024, 48(8): 67-78.
Hu Guang, Gao Huisheng, Xin Huanhai, et al.Quantification method for power system frequency strength considering voltage dynamics[J]. Automation of Electric Power Systems, 2024, 48(8): 67-78.
[23] Hu Guang, Xiao Yi, Xin Huanhai, et al.An extended impedance model for power electronics converters retaining explicit synchronization dynamics[J]. IEEE Transactions on Power Electronics, 2025, 40(1): 2355-2370.
[24] Zhong Weilin, Tzounas G, Milano F.Improving the power system dynamic response through a combined voltage-frequency control of distributed energy resources[J]. IEEE Transactions on Power Systems, 2022, 37(6): 4375-4384.
[25] Ai Cheng, Li Yitong, Zhao Ziwen, et al.An extension of grid-forming: a frequency-following voltage-forming inverter[J]. IEEE Transactions on Power Electronics, 2024, 39(10): 12118-12123.
[26] Fang Jingyang, Li Hongchang, Tang Yi, et al.On the inertia of future more-electronics power systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2019, 7(4): 2130-2146.
[27] Kundur P.Power System Stability and Control[M]. New York: McGraw-Hill, Inc, 1994.
[28] Gu Yunjie, Li Yitong, Zhu Yue, et al.Impedance-based whole-system modeling for a composite grid via embedding of frame dynamics[J]. IEEE Transa-ctions on Power Systems, 2021, 36(1): 336-345.
[29] Zhu Yue, Gu Yunjie, Li Yitong, et al.Participation analysis in impedance models: the grey-box approach for power system stability[J]. IEEE Transactions on Power Systems, 2021, 37(1): 343-353.
[30] Zhu Yue, Gu Yunjie, Li Yitong, et al.Impedance-based root-cause analysis: comparative study of impedance models and calculation of eigenvalue sensitivity[J]. IEEE Transactions on Power Systems, 2022, 38(2): 1642-1654.
[31] 郑乐, 郑佳杰. 构网型逆变器内部动态的扩展阻抗模态分析[J]. 电工技术学报, 2025, 40(9): 2712-2723, 2737.
Zheng Le, Zheng Jiajie.Extended impedance modal analysis of internal dynamics in grid-forming inverters[J]. Transactions of China Electrotechnical Society, 2025, 40(9): 2712-2723, 2737.
[32] 徐政. 新型电力系统背景下电网强度的合理定义及其计算方法[J]. 高电压技术, 2022, 48(10): 3805-3819.
Xu Zheng.Reasonable definition and calculation method of power grid strength under the background of new type power systems[J]. High Voltage Engin-eering, 2022, 48(10): 3805-3819.
[33] 张祥宇, 胡剑峰, 付媛, 等. 风储联合系统的虚拟惯量需求与协同支撑[J]. 电工技术学报, 2024, 39(3): 672-685.
Zhang Xiangyu, Hu Jianfeng, Fu Yuan, et al.Virtual inertia demand and collaborative support of wind power and energy storage system[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 672-685.
[34] 阮益闽, 宗启航, 姚伟, 等. 计及典型控制的风电场调频能力量化评估及影响因素分析[J]. 电力系统自动化, 2024, 48(8): 42-52.
Ruan Yimin, Zong Qihang, Yao Wei, et al.Quantitative assessment and analysis of influencing factors on frequency regulation capability of wind farms considering typical control[J]. Automation of Electric Power Systems, 2024, 48(8): 42-52.
[35] 赵冬梅, 宋晨铭, 冯向阳, 等. 100%新能源场景下考虑频率稳定约束的源网荷储一体化系统储能优化配置[J]. 电工技术学报, 2025, 40(7): 2146-2161.
Zhao Dongmei, Song Chenming, Feng Xiangyang, et al.The optimal configuration of energy storage in the source-grid-load-storage integrated system con-sidering frequency stability constraints in 100% new energy scenarios[J]. Transactions of China Electro-technical Society, 2025, 40(7): 2146-2161.
[36] Fan Lingling, Miao Zhixin.Time-domain measurement-based DQ-frame admittance model identification for inverter-based resources[J]. IEEE Transactions on Power Systems, 2021, 36(3): 2211-2221.
[37] 吴滨源, 李建文, 李永刚, 等. 并网逆变器dq阻抗灰箱辨识方法与应用[J]. 中国电机工程学报, 2022, 42(4): 1534-1546.
Wu Binyuan, Li Jianwen, Li Yonggang, et al.Gray-box identification method of grid-connected inverters dq impedance and its applications[J]. Proceedings of the CSEE, 2022, 42(4): 1534-1546.
[38] Li Yufei, Liao Yicheng, Zhao Liang, et al.Machine learning at the grid edge: data-driven impedance models for model-free inverters[J]. IEEE Transactions on Power Electronics, 2024, 39(8): 10465-10481.